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This photo of Comet C/2014 Q2 Lovejoy was taken in late December 2014 at an approximate magnitude of 5.6. Photo courtesy Wikimedia, photo by Paul Stewart.

Earthlings had their last chance for 8,000 years to see Comet Lovejoy Saturday night.

The opportunity to look up and see its green glow came when the comet was six days away from perihelion. On Jan. 30 the comet, formally known as Comet C/2014 Q2 Lovejoy, will be 193 million kilometers from the sun.

The comet actually passed closest to Earth on Jan. 7, when it was 70.2 million kilometers away.

It will be about 13,000 years before Comet Lovejoy is again close enough to Earth to be seen without the aid of a magnifying device.

How do scientists know how long it has been since a comet was visible with only the eyes from the surface of our planet?

The answer involves mathematics. Among the laws of planetary motion discovered by Johannes Kepler is the equation necessary to determine a comet’s period, or the amount of time needed to complete an orbit, if its semi-major axis is known. The semi-major axis of an ellipse, which is the shape that most objects in orbit around the sun follow, is best thought of as the radius of the ellipse at its two points that are most distant from each other.

This graphic shows the semi-major and semi-minor axes of an ellipse. Courtesy Wikimedia.

Kepler determined that the square of the ellipse’s period is equal to the cube of the semi-major axis’ length.

Another interesting feature of Comet Lovejoy’s orbit is its orientation relative to the plane of Earth’s and the other planets’ orbits. As Phil Plait explained at Bad Astronomy, the comet sits about 80 degrees off those trajectories.

The U.S. Senate again refused on Thursday to acknowledge the human role in climate change, voting down two proposals that would have forced members to go on record as recognizing scientific reality.

Senators first rejected an amendment to the underlying bill authorizing the KXL oil pipeline that specified that climate change is “real” and “caused by human activities” and “has already caused devastating problems in the United States and around the world.” The proposal, offered by Sen. Joe Manchin, D-W.Va., also included language that encouraged research into “clean fossil fuel technology.”

The Senate tabled the amendment, 53-46, with only one Republican – Mark Kirk of Illinois – voting with Democrats to allow floor debate on its merits.

Later, an amendment introduced by Sen. Bernie Sanders, I-Vt., that also acknowledged human impacts on the atmosphere and oceans and that emphasized the importance of developing non-fossil fuel energy sources was also tabled.

The chamber, with every one of 54 majority Republicans opposed to it, voted 56-42 to table it. Democratic senators Heidi Heitkamp of oil-producing state North Dakota and Claire McCaskill of Missouri also voted to deny consideration of its merits.

Majority leader Mitch McConnell, R-Ky., announced late Thursday night that the Senate would not consider additional amendments to S.1. A vote on whether to cut off floor debate on the bill itself is expected early next week.

President Barack Obama has threatened to veto any bill that interferes with his authority to decide whether or not to grant the permit required to construct the KXL pipeline across the U.S.-Canada border.

The century is only 14 years old, but the record for hottest year in recorded history has just been broken for the third time.

Scientists at the National Oceanic & Atmospheric Administration and NASA announced last week that, during 2014, the worldwide combined average air and sea temperature exceeded the average since 1880 by 0.69 degrees Celsius.

The two agencies’ reports confirm a similar conclusion announced by the Japan Meteorological Agency earlier in January.

An analysis of the new data by climatologist James Hansen of Columbia University and others concludes that the ten hottest years in the planet’s recorded climate history have occurred since 2000 and that the 15 hottest have occurred since 1998.

“This is the latest in a series of warm years, in a series of warm decades,” Dr. Gavin A. Schmidt, a climatologist and the director of NASA’s Goddard Institute of Space Studies, said in a statement. “While the ranking of individual years can be affected by chaotic weather patterns, the long-term trends are attributable to drivers of climate change that right now are dominated by human emissions of greenhouse gases.”

Overall, Earth’s average surface temperature has risen by 0.8 degrees Celsius since meteorological records were first kept 135 years ago.

This graph shows the annual mean surface temperature on Earth during every year since 1880. Courtesy NASA Goddard Institute for Space Studies.

Not all regions of the planet experienced the same degree of warmth last year. In the United States, for example, certain areas of the Midwest and along the East coast were cooler than average. But those cooler temperatures were outweighed by the broader swaths of the world that experienced hotter-than-normal temperatures.

Four U.S. states – Alaska, Arizona, California, and Nevada – experienced their warmest years in recorded history.

Individually, the global mean land temperature during 2014 was the fourth-highest on record. However, the 0.55 degree Celsius leap above the mean experienced by the seas drove the overall mean surface temperature to the all-time record. The extent to which sea temperatures exceeded the historic mean was unprecedented.

These graphs show the deviation from the norm of land and sea surface temperatures during 2014. Courtesy National Oceanic & Atmospheric Administration.

Emissions of carbon dioxide, a leading contributor to the warming of Earth’s climate, continue to rise. Data released earlier this month by the Scripps Institution of Oceanography at the University of California at San Diego indicates that the concentration of CO2 in the atmosphere surpassed 400 parts per million on Jan. 1, Jan. 3, and Jan. 7.

The first time it happened was in 2013, but the threshold was not crossed until May 2013. In 2014, the monthly average concentration of CO2 in the atmosphere reached 400 ppm in March, April, and June.

The current atmospheric concentration of carbon dioxide is higher than it has been in at least 800,000 years.

Astronomers from a university in Spain suggested in a paper published earlier this month that there may be at least two planets in our solar system beyond the orbit of Neptune, shown here in a 1989 image obtained by the Voyager 2 spacecraft. Image courtesy NASA.

A paper published earlier this month in a European journal proposes that the solar system may include two or more additional planets beyond the orbit of Neptune.

The hypothesis is based on a mathematical calculation of the expected orbital dynamics of other objects that orbit the sun in the vast region beyond our star’s outermost known planet.

Scientists have long understood that extreme trans-Neptunian objects should proceed in orbit on a path that has an inclination of zero degrees and an angle of perihelion of about zero degrees. The accepted theory also holds that the semi-major axis of ETNOs should be about 150 astronomical units.

The inclination of a celestial object’s orbit is the angular distance between that orbit and the ecliptic. An object’s perihelion is the point in the object’s orbit where it is closest to the sun. The semi-major axis of an orbit can best be thought of as the radius between the two points in an orbit that are most distant from each other.

In the cases of 12 of the ETNOs, the data indicates that their orbits do not comport with those expectations. For example, their semi-major axes vary between 150 AU and 525 AU and the average inclination of their orbits is about 20 degrees.

“This excess of objects with unexpected orbital parameters makes us believe that some invisible forces are altering the distribution of the orbital elements of the ETNO and we consider that the most probable explanation is that other unknown planets exist beyond Neptune and Pluto,” Carlos de la Fuente Marcos, an astrophysicist at the Complutense University of Madrid in Spain and a co-author of the study, said. “The exact number is uncertain, given that the data that we have is limited, but our calculations suggest that there are at least two planets, and probably more, within the confines of our solar system.”

Fuentes and two co-authors applied a phenomenon called the Kozai mechanism, a mathematical model that shows how a more distant celestial object affects the orbit of one that is closer to the sun, to achieve their hypothesis. The researchers applied the Kozai mechanism to a comet called 96P/Machholz1 and Jupiter as a model.

The analysis suggests that the only way the dozen ETNOs would demonstrate the orbital characteristics they do is if at least two more planets, larger than Earth, are farther out in space.

This conclusion is not consistent with the traditional view of the solar system, which holds that no planets in a circular orbit beyond Neptune are possible.

But other recent research indicates that the conventional view of the maximum size of our solar system may be incorrect. In 2014, for example, astronomers using the Atacama Large Millimeter Array in Chile documented the discovery of a star system about 450 light years away in which a planet-forming cloud of debris exists more than 100 AUs from the star.

Scientists have also confirmed the presence of at least two celestial objects far beyond Pluto with eccentric orbits that may be explained by the presence of a planet larger than Earth in the inner Oort cloud. Those dwarf planets – Sedna and 2012VP113 – have highly elongated orbits that, at perihelion, come no closer than 76 and 80 AUs from the sun and, at aphelion, are more than 900 AUs and more than 450 AUs away from our star.

This month’s paper appears in Monthly Notices of the Royal Astronomical Society. It builds on conclusions the same authors proposed in another paper published in the same journal in Sept. 2014.

Today’s New York Times includes an article that discusses a new study with bad news about the fate of Earth’s marine life.

The study finds that human activities may be causing historically unique damage to the oceans.

“Current ocean trends, coupled with terrestrial defaunation lessons, suggest that marine defaunation rates will rapidly intensify as human use of the oceans industrializes,” the abstract of the study, published in Science, said.

The NYT piece, written by the esteemed science writer Carl Zimmer, quoted a lead author of the Science paper, Douglas J. McCauley of the University of California at Santa Barbara, as saying that the researchers’ conclusions indicate that a mass marine extinction is possible.

The basic gist of the Science paper is that the same patterns of events that have led to the extinction of hundreds of terrestrial mega-fauna are also at work in the oceans. One of the biggest threats, as on land, is industrialization.

“There are factory farms in the sea and cattle-ranch-style feed lots for tuna,” Dr. Stephen R. Palumbi, a marine ecologist at Stanford University and a co-author of the paper, said. “Shrimp farms are eating up mangroves with an appetite akin to that of terrestrial farming, which consumed native prairies and forest. Stakes for seafloor mining claims are being pursued with gold-rush-like fervor, and 300-ton ocean mining machines and 750-foot fishing boats are now rolling off the assembly line to do this work.”

The paper’s authors also discuss the likely impacts of climate change.

A more detailed analysis of the Science paper will be posted here at a later date.